Techniques for behavioral pairing in a contact center system

ABSTRACT

Techniques for behavioral pairing in a contact center system are disclosed. In one particular embodiment, the techniques may be realized as a method for behavioral pairing in a contact center system comprising: determining, by at least one computer processor communicatively coupled to and configured to operate in the contact center system, a plurality of contacts available for connection to an agent; determining, by the at least one computer processor, a plurality of preferred contact-agent pairings among possible pairings between the agent and the plurality of contacts; selecting, by the at least one computer processor, one of the plurality of preferred contact-agent pairings according to a probabilistic network flow model; and outputting, by the at least one computer processor, the selected one of the plurality of preferred contact-agent pairings for connection in the contact center system.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.15/918,469, filed Mar. 12, 2018, now U.S. Pat. No. 10,244,118, issuedMar. 26, 2019, which is a continuation of U.S. patent application Ser.No. 15/691,106, filed Aug. 30, 2017, now U.S. Pat. No. 9,942,405, issuedApr. 10, 2018, which is a continuation of U.S. patent application Ser.No. 15/582,223, filed Apr. 28, 2017, now U.S. Pat. No. 9,930,180, issuedMar. 27, 2018, each of which is hereby incorporated by reference in itsentirety as if fully set forth herein.

This application is also related to U.S. patent application Ser. No.15/918,442, filed Mar. 12, 2018, now U.S. Pat. No. 10,116,800, issuedOct. 30, 2018, which is a continuation of U.S. patent application Ser.No. 15/582,223, filed Apr. 28, 2017, now U.S. Pat. No. 9,930,180, issuedMar. 27, 2018, each of which is hereby incorporated by reference in itsentirety as if fully set forth herein.

FIELD OF THE DISCLOSURE

This disclosure generally relates to pairing contacts and agents incontact centers and, more particularly, to techniques for behavioralpairing in a contact center system.

BACKGROUND OF THE DISCLOSURE

A typical contact center algorithmically assigns contacts arriving atthe contact center to agents available to handle those contacts. Attimes, the contact center may have agents available and waiting forassignment to inbound or outbound contacts (e.g., telephone calls,Internet chat sessions, email). At other times, the contact center mayhave contacts waiting in one or more queues for an agent to becomeavailable for assignment.

In some typical contact centers, contacts are assigned to agents orderedbased on time of arrival, and agents receive contacts ordered based onthe time when those agents became available. This strategy may bereferred to as a “first-in, first-out”, “FIFO”, or “round-robin”strategy. In other typical contact centers, other strategies may beused, such as “performance-based routing”, or a “PBR” strategy.

In other, more advanced contact centers, contacts are paired with agentsusing a “behavioral pairing”, or a “BP” strategy, under which contactsand agents may be deliberately (preferentially) paired in a fashion thatenables the assignment of subsequent contact-agent pairs such that whenthe benefits of all the assignments under a BP strategy are totaled theymay exceed those of FIFO and other strategies such as performance-basedrouting (“PBR”) strategies. BP is designed to t encourage balancedutilization (or a degree of utilization skew) of agents within a skillqueue while nevertheless simultaneously improving overall contact centerperformance beyond what FIFO or PBR methods will allow. This is aremarkable achievement inasmuch as BP acts on the same calls and sameagents as FIFO or PBR methods, utilizes agents approximately evenly asFIFO provides, and yet improves overall contact center performance. BPis described in, e.g., U.S. Pat. No. 9,300,802, which is incorporated byreference herein. Additional information about these and other featuresregarding the pairing or matching modules (sometimes also referred to as“SATMAP”, “routing system”, “routing engine”, etc.) is described in, forexample, U.S. Pat. No. 8,879,715, which is incorporated by referenceherein.

A BP strategy may use a one-dimensional ordering of agents and contacttypes in conjunction with a diagonal strategy for determining preferredpairings. However, this strategy may restrict or otherwise limit thetype and number of variables that a BP strategy could optimize, or theamount to which one or more variables could be optimized, given moredegrees of freedom.

In view of the foregoing, it may be understood that there is a need fora system that enables improving the efficiency and performance ofpairing strategies that are designed to choose among multiple possiblepairings such as a BP strategy.

SUMMARY OF THE DISCLOSURE

Techniques for behavioral pairing in a contact center system aredisclosed. In one particular embodiment, the techniques may be realizedas a method for behavioral pairing in a contact center systemcomprising: determining, by at least one computer processorcommunicatively coupled to and configured to operate in the contactcenter system, a plurality of contacts available for connection to anagent; determining, by the at least one computer processor, a pluralityof preferred contact-agent pairings among possible pairings between theagent and the plurality of contacts; selecting, by the at least onecomputer processor, one of the plurality of preferred contact-agentpairings according to a probabilistic network flow model; andoutputting, by the at least one computer processor, the selected one ofthe plurality of preferred contact-agent pairings for connection in thecontact center system.

In accordance with other aspects of this particular embodiment, theprobabilistic network flow model may be a network flow model forbalancing agent utilization, a network flow model for applying an amountof agent utilization skew, or a network flow model for optimizing anoverall expected value of at least one contact center metric. Also, theat least one contact center metric may be at least one of revenuegeneration, customer satisfaction, and average handle time.

In accordance with other aspects of this particular embodiment, theprobabilistic network flow model may be a network flow model constrainedby agent skills and contact skill needs. Also, the probabilistic networkflow model may be adjusted to minimize agent utilization imbalanceaccording to the constraints of the agent skills and the contact skillneeds.

In accordance with other aspects of this particular embodiment, theprobabilistic network flow model may incorporate expected payoff valuesbased on an analysis of at least one of historical contact-agent outcomedata and contact attribute data.

In another particular embodiment, the techniques may be realized as asystem for behavioral pairing in a contact center system comprising atleast one computer processor communicatively coupled to and configuredto operate in the contact center system, wherein the at least onecomputer processor is further configured to perform the steps in theabove-discussed method.

In another particular embodiment, the techniques may be realized as anarticle of manufacture for behavioral pairing in a contact center systemcomprising a non-transitory processor readable medium and instructionsstored on the medium, wherein the instructions are configured to bereadable from the medium by at least one computer processorcommunicatively coupled to and configured to operate in the contactcenter system and thereby cause the at least one computer processor tooperate to perform the steps in the above-discussed method.

The present disclosure will now be described in more detail withreference to particular embodiments thereof as shown in the accompanyingdrawings. While the present disclosure is described below with referenceto particular embodiments, it should be understood that the presentdisclosure is not limited thereto. Those of ordinary skill in the arthaving access to the teachings herein will recognize additionalimplementations, modifications, and embodiments, as well as other fieldsof use, which are within the scope of the present disclosure asdescribed herein, and with respect to which the present disclosure maybe of significant utility.

BRIEF DESCRIPTION OF THE DRAWINGS

To facilitate a fuller understanding of the present disclosure,reference is now made to the accompanying drawings, in which likeelements are referenced with like numerals. These drawings should not beconstrued as limiting the present disclosure, but are intended to beillustrative only.

FIG. 1 shows a block diagram of a contact center according toembodiments of the present disclosure.

FIG. 2 shows an example of a BP payout matrix according to embodimentsof the present disclosure.

FIG. 3 depicts an example of a naïve BP utilization matrix according toembodiments of the present disclosure.

FIG. 4A shows an example of a BP skill-based payout matrix according toembodiments of the present disclosure.

FIG. 4B shows an example of a BP network flow according to embodimentsof the present disclosure.

FIG. 4C shows an example of a BP network flow according to embodimentsof the present disclosure.

FIG. 4D shows an example of a BP network flow according to embodimentsof the present disclosure.

FIG. 4E shows an example of a BP network flow according to embodimentsof the present disclosure.

FIG. 4F shows an example of a BP network flow according to embodimentsof the present disclosure.

FIG. 4G shows an example of a BP network flow according to embodimentsof the present disclosure.

FIG. 5A depicts an example of a BP skill-based payout matrix accordingto embodiments of the present disclosure.

FIG. 5B shows an example of a BP network flow according to embodimentsof the present disclosure.

FIG. 5C shows an example of a BP network flow according to embodimentsof the present disclosure.

FIG. 5D shows an example of a BP network flow according to embodimentsof the present disclosure.

FIG. 5E shows an example of a BP network flow according to embodimentsof the present disclosure.

FIG. 5F shows an example of a BP network flow according to embodimentsof the present disclosure.

FIG. 5G shows an example of a BP network flow according to embodimentsof the present disclosure.

FIG. 5H shows an example of a BP network flow according to embodimentsof the present disclosure.

FIG. 5I shows an example of a BP network flow according to embodimentsof the present disclosure.

FIG. 6 depicts a flow diagram of a BP skill-based payout matrix methodaccording to embodiments of the present disclosure.

FIG. 7A shows a flow diagram of a BP network flow method according toembodiments of the present disclosure.

FIG. 7B shows a flow diagram of a BP network flow method according toembodiments of the present disclosure.

FIG. 8 shows a flow diagram of a BP network flow method according toembodiments of the present disclosure.

FIG. 9 shows a flow diagram of a BP network flow method according toembodiments of the present disclosure.

DETAILED DESCRIPTION

A typical contact center algorithmically assigns contacts arriving atthe contact center to agents available to handle those contacts. Attimes, the contact center may have agents available and waiting forassignment to inbound or outbound contacts (e.g., telephone calls,Internet chat sessions, email). At other times, the contact center mayhave contacts waiting in one or more queues for an agent to becomeavailable for assignment.

In some typical contact centers, contacts are assigned to agents orderedbased on time of arrival, and agents receive contacts ordered based onthe time when those agents became available. This strategy may bereferred to as a “first-in, first-out”, “FIFO”, or “round-robin”strategy. In other typical contact centers, other strategies may beused, such as “performance-based routing”, or a “PBR” strategy.

In other, more advanced contact centers, contacts are paired with agentsusing a “behavioral pairing”, or a “BP” strategy, under which contactsand agents may be deliberately (preferentially) paired in a fashion thatenables the assignment of subsequent contact-agent pairs such that whenthe benefits of all the assignments under a BP strategy are totaled theymay exceed those of FIFO and other strategies such as performance-basedrouting (“PBR”) strategies. BP is designed to encourage balancedutilization (or a degree of utilization skew) of agents within a skillqueue while nevertheless simultaneously improving overall contact centerperformance beyond what FIFO or PBR methods will allow. This is aremarkable achievement because BP acts on the same calls and same agentsas FIFO or PBR methods, utilizes agents approximately evenly as FIFOprovides, and yet improves overall contact center performance. BP isdescribed in, e.g., U.S. Pat. No. 9,300,802, which is incorporated byreference herein. Additional information about these and other featuresregarding the pairing or matching modules (sometimes also referred to as“SATMAP”, “routing system”, “routing engine”, etc.) is described in, forexample, U.S. Pat. No. 8,879,715, which is incorporated by referenceherein.

A BP strategy may use a one-dimensional ordering of agents and contacttypes in conjunction with a diagonal strategy for determining preferredpairings. However, this strategy may restrict or otherwise limit thetype and number of variables that a BP strategy could optimize, or theamount to which one or more variables could be optimized, given moredegrees of freedom.

In view of the foregoing, it may be understood that there is a need fora system that enables improving the efficiency and performance ofpairing strategies that are designed to choose among multiple possiblepairings such as a BP strategy. Such a system may offer myriad benefits,including, in some embodiments, optimization based on comparativeadvantages at runtime; maintenance of uniform or approximately uniformutilization of agents; consolidation of models across skills into asingle coherent model or a smaller number of coherent models; creationof more complex, sophisticated, and capable models; etc. As described indetail below, the techniques may be multidimensional (e.g.,multivariate) in nature, and may use linear programming, quadraticprogramming, or other optimization techniques for determining preferredcontact-agent pairings. Examples of these techniques are described in,for example, Cormen et al., Introduction to Algorithms, 3rd ed., at708-68 and 843-897 (Ch. 26. “Maximum Flow” and Ch. 29 “LinearProgramming”) (2009), and Nocedal and Wright, Numerical Optimization, at448-96 (2006), which are hereby incorporated by reference herein.

FIG. 1 shows a block diagram of a contact center system 100 according toembodiments of the present disclosure. The description herein describesnetwork elements, computers, and/or components of a system and methodfor simulating contact center systems that may include one or moremodules. As used herein, the term “module” may be understood to refer tocomputing software, firmware, hardware, and/or various combinationsthereof. Modules, however, are not to be interpreted as software whichis not implemented on hardware, firmware, or recorded on a processorreadable recordable storage medium (i.e., modules are not software perse). It is noted that the modules are exemplary. The modules may becombined, integrated, separated, and/or duplicated to support variousapplications. Also, a function described herein as being performed at aparticular module may be performed at one or more other modules and/orby one or more other devices instead of or in addition to the functionperformed at the particular module. Further, the modules may beimplemented across multiple devices and/or other components local orremote to one another. Additionally, the modules may be moved from onedevice and added to another device, and/or may be included in bothdevices.

As shown in FIG. 1, the contact center system 100 may include a centralswitch 110. The central switch 110 may receive incoming contacts (e.g.,callers) or support outbound connections to contacts via atelecommunications network (not shown). The central switch 110 mayinclude contact routing hardware and software for helping to routecontacts among one or more contact centers, or to one or more PBX/ACDsor other queuing or switching components, including otherInternet-based, cloud-based, or otherwise networked contact-agenthardware or software-based contact center solutions.

The central switch 110 may not be necessary such as if there is only onecontact center, or if there is only one PBX/ACD routing component, inthe contact center system 100. If more than one contact center is partof the contact center system 100, each contact center may include atleast one contact center switch (e.g., contact center switches 120A and120B). The contact center switches 120A and 120B may be communicativelycoupled to the central switch 110. In embodiments, various topologies ofrouting and network components may be configured to implement thecontact center system.

Each contact center switch for each contact center may becommunicatively coupled to a plurality (or “pool”) of agents. Eachcontact center switch may support a certain number of agents (or“seats”) to be logged in at one time. At any given time, a logged-inagent may be available and waiting to be connected to a contact, or thelogged-in agent may be unavailable for any of a number of reasons, suchas being connected to another contact, performing certain post-callfunctions such as logging information about the call, or taking a break.

In the example of FIG. 1, the central switch 110 routes contacts to oneof two contact centers via contact center switch 120A and contact centerswitch 120B, respectively. Each of the contact center switches 120A and120B are shown with two agents each. Agents 130A and 130B may be loggedinto contact center switch 120A, and agents 130C and 130D may be loggedinto contact center switch 120B.

The contact center system 100 may also be communicatively coupled to anintegrated service from, for example, a third party vendor. In theexample of FIG. 1, BP module 140 may be communicatively coupled to oneor more switches in the switch system of the contact center system 100,such as central switch 110, contact center switch 120A, or contactcenter switch 120B. In some embodiments, switches of the contact centersystem 100 may be communicatively coupled to multiple BP modules. Insome embodiments, BP module 140 may be embedded within a component of acontact center system (e.g., embedded in or otherwise integrated with aswitch, or a “BP switch”). The BP module 140 may receive informationfrom a switch (e.g., contact center switch 120A) about agents loggedinto the switch (e.g., agents 130A and 130B) and about incoming contactsvia another switch (e.g., central switch 110) or, in some embodiments,from a network (e.g., the Internet or a telecommunications network) (notshown).

A contact center may include multiple pairing modules (e.g., a BP moduleand a FIFO module) (not shown), and one or more pairing modules may beprovided by one or more different vendors. In some embodiments, one ormore pairing modules may be components of BP module 140 or one or moreswitches such as central switch 110 or contact center switches 120A and120B. In some embodiments, a BP module may determine which pairingmodule may handle pairing for a particular contact. For example, the BPmodule may alternate between enabling pairing via the BP module andenabling pairing with the FIFO module. In other embodiments, one pairingmodule (e.g., the BP module) may be configured to emulate other pairingstrategies. For example, a BP module, or a BP component integrated withBP components in the BP module, may determine whether the BP module mayuse BP pairing or emulated FIFO pairing for a particular contact. Inthis case, “BP on” may refer to times when the BP module is applying theBP pairing strategy, and “BP off” may refer to other times when the BPmodule is applying a different pairing strategy (e.g., FIFO).

In some embodiments, regardless of whether pairing strategies arehandled by separate modules, or if some pairing strategies are emulatedwithin a single pairing module, the single pairing module may beconfigured to monitor and store information about pairings made underany or all pairing strategies. For example, a BP module may observe andrecord data about FIFO pairings made by a FIFO module, or the BP modulemay observe and record data about emulated FIFO pairings made by a BPmodule operating in FIFO emulation mode.

FIG. 2 shows an example of a BP payout matrix 200 according toembodiments of the present disclosure. In this simplified, hypotheticalcomputer-generated model of a contact center system, there are threeagents (Agents 201, 202, and 203), and there are three contact types(Contact Types 211, 212, and 213). Each cell of the matrix indicates the“payout,” or the expected outcome or expected value of a contact-agentinteraction between a particular agent and a contact of the indicatedcontact type. In real-world contact center systems, there could bedozens of agents, hundreds of agents, or more, and there could be dozensof contact types, hundreds of contact types, or more.

In BP payout matrix 200, the payout for an interaction between Agent 201and a contact of Contact Type 211 is 0.30, or 30%. The other payouts forAgent 201 are 0.28 for Contact Type 212 and 0.15 for Contact Type 213.The payouts for Agent 202 are 0.30 for Contact Type 211, 0.24 forContact Type 212, and 0.10 for Contact Type 213. The payouts for Agent203 are 0.25 for Contact Type 211, 0.20 for Contact Type 212, and 0.09for Contact Type 213.

A payout could represent the expected value for any of a variety ofdifferent metrics or optimized variables. Examples of optimizedvariables include conversion rates on sales, customer retention rates,customer satisfaction rates, average handle time measurements, etc., orcombinations of two or more metrics. For example, if BP payout matrix200 models a retention queue in a contact center system, each payout mayrepresent the likelihood that an agent will “save” or retain a customerof a particular contact type, e.g., there is a 0.30 (or 30%) chance thatAgent 201 will save a contact determined to be of Contact Type 211.

In some embodiments, the BP payout matrix 200 or other similarcomputer-generated model of the contact center system may be generatedusing historical contact-agent interaction data. For example, they BPpayout matrix 200 may incorporate a rolling window several weeks,several months, several years, etc. of historical data to predict orotherwise estimate the payouts for a given interaction between an agentand a contact type. As agent workforces change, the model may be updatedto reflect the changes to the agent workforce, including hiring newagents, letting existing agents go, or training existing agents on newskills. Contact types may be generated based on information aboutexpected contacts and existing customers, such as customer relationshipmanagement (CRM) data, customer attribute data, third-party consumerdata, contact center data, etc., which may include various types of datasuch as demographic and psychographic data, and behavioral data such aspast purchases or other historical customer information. The BP payoutmatrix 200 may be updated in real time or periodically, such as hourly,nightly, weekly, etc. to incorporate new contact-agent interaction dataas it becomes available.

FIG. 3 depicts an example of a naïve BP utilization matrix 300 accordingto embodiments of the present disclosure. As for the BP payout matrix200 (FIG. 2), this simplified, hypothetical computer-generated model ofa contact center system, there are three agents (Agents 201, 202, and203), and there are three contact types (Contact Types 211, 212, and213). In real-world contact center systems, there could be dozens ofagents, hundreds of agents, or more, and there could be dozens ofcontact types, hundreds of contact types, or more.

Under a BP strategy, agents are preferentially paired with contacts ofparticular contact types according to the computer-generated BP models.In an L1 environment, the contact queue is empty, and multiple agentsare available, idle, or otherwise ready and waiting for connection to acontact. For example, in a chat context, an agent may have a capacity tochat with multiple contacts concurrently. In these environments, anagent may be ready for connection to one or more additional contactswhile multitasking in one or more other channels such as email and chatconcurrently.

In some embodiments, when a contact arrives at the queue or othercomponent of the contact center system, the BP strategy analyzesinformation about the contact to determine the contact's type (e.g., acontact of Contact Type 211, 212, or 213). The BP strategy determineswhich agents are available for connection to the contact and selects,recommends, or otherwise outputs a pairing instruction for the mostpreferred available agent.

In an L2 environment, multiple contacts are waiting in queue forconnection to an agent, and none of the agents is available, free, orotherwise ready for connection to a contact. The BP strategy analyzesinformation about each contact to determine each contact's type (e.g.,one or contacts of Contact Types 211, 212, or 213). In some embodiments,when an agent becomes available, the BP strategy determines whichcontacts are available for connection to the agent and selects,recommends, or otherwise outputs a pairing instruction for the mostpreferred available contact.

As shown in the header row of the naïve BP utilization matrix 300, eachagent has an expected availability or a target utilization. In thisexample, the BP strategy is targeting a balanced agent utilization of ⅓(“0.33”) for each of the three Agents 201, 202, and 203. Thus, overtime, each agent is expected to be utilized equally, or approximatelyequally. This configuration of BP is similar to FIFO insofar as both BPand FIFO target an unbiased, or balanced, agent utilization.

This configuration of BP is dissimilar to performance-based routing(PBR) insofar as PBR targets a skewed, or unbalanced, agent utilization,intentionally assigning a disproportionate number of contacts torelatively higher-performing agents. Other configurations of BP may besimilar to PBR insofar as other BP configurations may also target askewed agent utilization. Additional information about these and otherfeatures regarding skewing agent or contact utilization (e.g., “kappa”and “rho” functionality) is described in, for example, U.S. patentapplication Ser. Nos. 14/956,086 and 14/956,074, which are herebyincorporated by reference herein.

As shown in the header column of the naïve BP utilization matrix 300,each contact type has an expected availability (e.g., frequency ofarrival) or a target utilization. In this example, contacts of ContactType 211 are expected to arrive 50% (“0.50”) of the time, contacts ofContact Type 212 are expected to arrive 30% (“0.30”) of the time, andcontacts of type Contact Type 212 are expected to arrive the remaining20% (“0.20”) of the time.

Each cell of the matrix indicates the target utilization, or expectedfrequency, of a contact-agent interaction between a particular agent anda contact of the indicated contact type. In the example of naïve BPutilization matrix 300, agents are expected to be assigned equally toeach contact type according to each contact type's frequency. Contactsof Contact Type 211 are expected to arrive in the queue 50% of the time,with approximately one-third of these contacts assigned to each ofAgents 201, 202, and 203. Overall, contact-agent interactions betweenContact Type 211 and Agent 201 are expected to occur approximately 16%(“0.16”) of the time, between Contact Type 211 and Agent 202approximately 16% of the time, and between Contact Type 211 and Agent203 approximately 16% of the time. Similarly, interactions betweencontacts of Contact Type 212 (30% frequency) and each of the Agents201-203 are expected to occur approximately 10% (“0.01”) of the timeeach, and interactions between contacts of Contact Type 213 (20%frequency) and each of the Agents 201-203 are expected to occurapproximately 7% (“0.07”) of the time.

The naïve BP utilization matrix 300 also represents approximately thesame distribution of contact-agent interactions that would arise under aFIFO pairing strategy, under which each contact-agent interaction wouldbe equally likely (normalized for the frequency of each contact type).Under naïve BP and FIFO, the targeted (and expected) utilization of eachagent is equal: one-third of the contact-agent interactions to each ofthe three Agents 201-203.

Taken together, the BP payout matrix 200 (FIG. 2) and the naïve BPutilization matrix 300 enable determining an expected overallperformance of the contact center system, by computing an average payoutweighted according to the frequency distribution of each contact-agentinteraction shown in the naïve BP utilization matrix 300:(0.30+0.30+0.25)(0.50)(⅓)+(0.28+0.24+0.20)(0.30)(⅓)+(0.15+0.10+0.09)(0.20)(⅓)0.24. Thus, the expected performance of the contact center system undernaïve BP or FIFO is approximately 0.24 or 24%. If the payouts represent,for example, retention rates, the expected overall performance would bea 24% save rate.

FIGS. 4A-4G show an example of a more sophisticated BP payout matrix andnetwork flow. In this simplified, hypothetical contact center, agents orcontact types may have different combinations of one or more skills(i.e., skill sets), and linear programming-based network flowoptimization techniques may be applied to increase overall contactcenter performance while maintaining a balanced utilization acrossagents and contacts.

FIG. 4A shows an example of a BP skill-based payout matrix 400Aaccording to embodiments of the present disclosure. The hypotheticalcontact center system represented in BP skill-based payout matrix 400Ais similar to the contact center system represented in BP payout matrix200 (FIG. 2) insofar as there are three agents (Agents 401, 402, and403) having an expected availability/utilization of approximatelyone-third or 0.33 each, and there are three contact types (Contact Types411, 412, and 413) having an expected frequency/utilization ofapproximately 25% (0.15+0.10), 45% (0.15+0.30), and 30% (0.20+0.10),respectively.

However, in the present example, each agent has been assigned, trained,or otherwise made available to a particular skill (or, in other examplecontact center systems, sets of multiple skills). Examples of skillsinclude broad skills such as technical support, billing support, sales,retention, etc.; language skills such as English, Spanish, French, etc.;narrower skills such as “Level 2 Advanced Technical Support,” technicalsupport for Apple iPhone users, technical support for Google Androidusers, etc.; and any variety of other skills.

Agent 401 is available for contacts requiring at least Skill 421, Agent402 is available for contacts requiring at least Skill 422, and Agent403 is available for contacts requiring at least Skill 423.

Also in the present example, contacts of each type may arrive requiringone or more of Skills 421-423. For example, a caller to a call centermay interact with an Interactive Voice Response (IVR) system, touch-tonemenu, or live operator to determine which skills the particularcaller/contact requires for the upcoming interaction. Another way toconsider a “skill” of a contact type is a particular need the contacthas, such as buying something from an agent with a sales skill, ortroubleshooting a technical issue with an agent having a technicalsupport skill.

In the present example, 0.15 or 15% of contacts are expected to be ofContact Type 411 and require Skill 421 or Skill 422; 0.15 or 15% ofcontacts are expected to be of Contact Type 412 and require Skill 421 or422; 0.20 or 20% of contacts are expected to be of Contact Type 413 andrequire Skill 421 or 422; 0.10 or 10% of contacts are expected to be ofContact Type 411 and require Skill 422 or Skill 423; 0.30 or 30% ofcontacts are expected to be of Contact Type 412 and require Skill 422 orSkill 423; 0.10 or 10% of contacts are expected to be of Contact Type413 and require Skill 422 or Skill 423.

In some embodiments, Agents may be required to have the union of allskills determined to be required by a particular contact (e.g., Spanishlanguage skill and iPhone technical support skill). In some embodiments,some skills may be preferred but not required (i.e., if no agents havingthe skill for iPhone technical support are available immediately orwithin a threshold amount of time, a contact may be paired with anavailable Android technical support agent instead).

Each cell of the matrix indicates the payout of a contact-agentinteraction between a particular agent with a particular skill or skillset and a contact with a particular type and need (skill) or set ofneeds (skill set). In the present example, Agent 401, which has Skill421, may be paired with contacts of any Contact Type 411, 412 or 413when they require at least Skill 421 (with payouts 0.30, 0.28, and 0.15,respectively). Agent 402, which has Skill 422, may be paired withcontacts of any Contact Type 411, 412, or 413 when they require at leastSkill 422 (with payouts 0.30, 0.24, 0.10, 0.30, 0.24, and 0.10,respectively). Agent 403, which has Skill 423, may be paired withcontacts of any Contact Type 411, 412, or 413 when they require at leastSkill 423 (with payouts 0.25, 0.20, and 0.09, respectively).

Empty cells represent combinations of contacts and agents that would notbe paired under this BP pairing strategy. For example, Agent 401, whichhas Skill 421, would not be paired with contacts that do not require atleast Skill 421. In the present example, the 18-cell payout matrixincludes 6 empty cells, and the 12 non-empty cells represent 12 possiblepairings.

FIG. 4B shows an example of a BP network flow 400B according toembodiments of the present disclosure. BP network flow 400B shows Agents401-403 as “sources” on the left side of the network (or graph) andContact Types 411-413 for each skill set as “sinks” on the right side ofthe network. Each edge in BP network flow 400B represents a possiblepairing between an agent and a contact having a particular type and setof needs (skills). For example, edge 401A represents a contact-agentinteraction between Agent 401 and contacts of Contact Type 411 requiringSkill 421 or Skill 422. Edges 401B, 401C, 402A-F, and 403A-C representthe other possible contact-agent pairings for their respective agentsand contact types/skills as shown.

FIG. 4C shows an example of a BP network flow 400C according toembodiments of the present disclosure. BP network flow 400C is anetwork/graph representation of BP payout matrix 400A (FIG. 4A). BPnetwork flow 400C is identical to BP network flow 400B (FIG. 4B) except,for clarity, the identifiers for each edge are not shown, and instead itshows the payout for each edge, e.g., 0.30 on edge 401A, 0.28 on edge401B, and 0.15 on edge 401C for Agent 401, and the corresponding payoutsfor each edge for Agents 402 and 403.

FIG. 4D shows an example of a BP network flow 400D according toembodiments of the present disclosure. BP network flow 400D is identicalto BP network flow 400C (FIG. 4C) except, for clarity, the skills foreach agent 401-403 are not shown, and instead it shows the relative“supplies” provided by each agent and “demands” required by each contacttype/skill combination. Each agent provides a “supply” equivalent to theexpected availability or target utilization of each agent (one-thirdeach, for a total supply of 1 or 100%). Each contact type/skill demandsan amount of agent supply equivalent to the expected frequency or targetutilization of each contact type/skill (0.15, 0.15, 0.20, 0.10, 0.30,0.10, respectively, for a total demand of 1 or 100%). In this example,the total supply and demand are normalized or otherwise configured toequal one another, and the capacity or bandwidth along each edge isconsidered infinite or otherwise unlimited (i.e., an edge may describe“who can be paired with whom,” not “how much,” or “how many times”). Inother embodiments, there may be a supply/demand imbalance, or there maybe quotas or otherwise limited capacities set for some or all edges.

FIG. 4E shows an example of a BP network flow 400E according toembodiments of the present disclosure. BP network flow 400E is identicalto BP network flow 400D (FIG. 4D) except, for ease of representation,the supplies and demands have been scaled by a factor of 3000. In doingso, the supply for each agent is shown to be 1000 instead of one-third,and the total supply is shown to be 3000. Similarly, the relativedemands for each contact type/skill set has been scaled and total 3000as well. In some embodiments, no scaling occurs. In other embodiments,the amount of scaling may vary and be greater or smaller than 3000.

FIG. 4F shows an example of a BP network flow 400F according toembodiments of the present disclosure. BP network flow 400F is identicalto BP network flow 400E (FIG. 4E) except, for clarity, the payouts alongeach edge are not shown, and instead it shows one solution for the BPnetwork flow 400F. In some embodiments, a “maximum flow” or “max flow”algorithm, or other linear programming algorithm, may be applied to theBP network flow 400F to determine one or more solutions for optimizingthe “flow” or “allocation” of the supplies (sources) to satisfy thedemands (sinks), which may balance utilization of agents and contacts.

In some embodiments, the objective may also be to maximize the overallexpected value for the metric or metrics to be optimized. For example,in a sales queue, the metric to optimize may be conversion rate, and themax flow objective is to maximize the overall expected conversion rate.In environments where multiple max flow solutions are available, onetechnique for selecting a solution may be to select the “maximum cost”or “max cost” solution, i.e., the solution that results in the highestoverall payoffs under max flow.

In this example, Agents 401-403 represent the sources, and Contact Types411-413 with various skill set combinations represent the sinks. In somecontact center environments, such as an L2 (contact surplus)environment, the network flow may be reversed, so that contacts waitingin queue are the sources providing supplies, and the possible agentsthat may become available are the sinks providing demands.

BP network flow 400F shows an optimal flow solution determined by a BPmodule or similar component. According to this solution, of which therecould be several to choose among, or to be selected at random, edge 401A(from Agent 401 to Contact Type 411 with Skills 421 and 422) has anoptimal flow of 0; edge 401B (from Agent 401 to Contact Type 412 withSkills 421 and 422) has an optimal flow of 400; and edge 401C (fromAgent 401 to Contact Type 413 with Skills 421 and 422) has an optimalflow of 600. Similarly, the optimal flows for edges 402A-F for Agent 402are 450, 50, 0, 300, 200, and 0, respectively; and the optimal flows foredges 403A-C for Agent 403 are 0, 700, and 300, respectively. Asexplained in detail below, this optimal flow solution describes therelative proportion of contact-agent interactions (or the relativelikelihoods of selecting particular contact-agent interactions) thatwill achieve the target utilization of agents and contacts while alsomaximizing the expected overall performance of the contact center systemaccording to the payouts for each pair of agent and contact type/skillset.

FIG. 4G shows an example of a BP network flow 400G according toembodiments of the present disclosure. BP network flow 400G is identicalto BP network flow 400F (FIG. 4F) except, for clarity, edges for whichthe optimal flow solution was determined to be 0 have been removed.Under a BP strategy, an agent will not be preferably paired with acontact type for which the optimal flow solution was determined to be 0,despite having complementary skills and a nonzero payout.

In this example, edges 401A, 402C, 402F, and 403A have been removed. Theremaining edges represent preferred pairings. Thus, in an L1 (agentsurplus) environment, when a contact arrives, it may be preferablypaired with one of the agents for which there is a preferred pairingavailable. For example, a contact of Contact Type 411 with Skills 421and 422 may always be preferably paired with Agent 402, demanding 450units of Agent 402's total supply (availability). For another example, acontact of Contact Type 412 with Skills 421 and 422 may be preferablypaired with Agent 401 some of the time and with Agent 402 some of thetime. This contact has a total demand of 450 (based on the expectedfrequency that this type of contact/skill will arrive), and it demands400 units of supply from Agent 401, and the remaining 50 units of supplyfrom Agent 402.

In some embodiments, when this contact of type/skill arrives, the BPmodule or similar component may select either Agent 401 or 402 accordingto the relative demands (400 and 50) made of each agent. For example, apseudorandom number generator may be used to select Agent 401 or 402randomly, with the random selection weighted according to the relativedemands. Thus, for each contact of this type/skill, there is a 400/450(≈89%) chance of selecting Agent 401 as the preferred pairing, and50/450 (≈11%) chance of selecting Agent 402 as the preferred pairing.Over time, as many contacts of this type/skill have been paired usingthe BP strategy, approximately 89% of them may have been preferablypaired to Agent 401, and the remaining 11% of them may have beenpreferably paired to Agent 402. In some embodiments, an agent's overalltarget utilization, or target utilization per contact type/skill, may bethe agent's “bandwidth” for receiving a proportional percentage ofcontacts.

For this BP network flow 400G with this solution, the total supply fromall of the agents is expected to meet the total demand from all of thecontacts. Thus, the target utilization (here, a balanced utilization) ofall agents may be achieved, while also achieving a higher expectedoverall performance in the contact center system according to thepayouts and the relative allocations of agents to contacts along theedges with those payouts.

FIGS. 5A-I show an example of another BP payout matrix and network flow.For some configurations of agents and contact types with variouscombinations of skills, it is possible that the optimal or max flow fora given BP network flow may not completely balance supply and demand.The present example is similar to the example of FIGS. 4A-4G, exceptthis configuration of agents and contact types initially leads to animbalanced supply and demand. In this simplified, hypothetical contactcenter, quadratic programming-based techniques for adjusting targetutilization may be applied in conjunction with linear programming-basednetwork flow optimization techniques to increase overall contact centerperformance while maintaining an optimally skewed utilization acrossagents and contacts to accommodate the imbalanced configuration ofagents and contact types.

FIG. 5A depicts an example of a BP skill-based payout matrix 500Aaccording to embodiments of the present disclosure. The hypotheticalcontact center system represented in BP skill-based payout matrix 500Ais similar to the contact center system represented in BP skill-basedpayout matrix 400A (FIG. 4) insofar as there are three agents (Agents501, 502, and 503) having an initial expected availability/utilizationof approximately one-third or 0.33 each. There are two contact types(Contact Types 511 and 512) having an expected frequency/utilization ofapproximately 40% (0.30+0.10) and 60% (0.30+0.30), respectively.

In the present example, Agent 501 has been assigned, trained, orotherwise made available to Skills 521 and 522, and Agents 502 and 503to Skill 522 only. For example, if Skill 521 represented a Frenchlanguage skill, and Skill 522 represented a German language skill, Agent501 could be assigned to contacts requiring either French or German,whereas Agents 502 and 503 could be assigned only to contacts requiringGerman and not to contacts requiring French.

In the present example, 0.30 or 30% of contacts are expected to be ofContact Type 511 and require Skill 521; 0.30 or 30% of contacts areexpected to be of Contact Type 512 and require Skill 521; 0.10 or 10% ofcontacts are expected to be of Contact Type 511 and require Skill 522;and 0.30 or 30% of contacts are expected to be of Contact Type 512 andrequire Skill 522.

In the present example, Agent 501 may be paired with any contact (withpayouts 0.30, 0.28, 0.30, and 0.28, as shown in BP skill-based payoutmatrix 500A). Agents 502 and 503, which have Skill 522 only, may bepaired with contacts of either Contact Type 511 and 512 when theyrequire at least Skill 522 (with payouts 0.30, 0.24, 0.25, and 0.20, asshown in BP skill-based payout matrix 500A). As indicated by the emptycells in BP skill-based payout matrix 500A, Agents 502 and 503 would notbe paired with contacts requiring only Skill 521. The 12-cell payoutmatrix includes 4 empty cells, and the 8 non-empty cells represent 8possible pairings.

FIG. 5B shows an example of a BP network flow 500B according toembodiments of the present disclosure. Similar to BP network flow 400B(FIG. 4B), BP network flow 500B shows Agents 501-503 as sources on theleft side of the network and Contact Types 512 and 5123 for each skillset as sinks on the right side of the network. Each edge in BP networkflow 500B represents a possible pairing between an agent and a contacthaving a particular type and set of needs (skills). Edges 501A-D,502A-B, and 503A-B represent the possible contact-agent pairings fortheir respective agents and contact types/skills as shown.

FIG. 5C shows an example of a BP network flow 500C according toembodiments of the present disclosure. BP network flow 500C is a networkrepresentation of BP payout matrix 500A (FIG. 5A). For clarity, theidentifiers for each edge are not shown, and instead it shows the payoutfor each edge, e.g., 0.30 on edges 501A and 501D, and 0.28 on edges 501Band 501C, and the corresponding payouts for each edge for Agents 502 and503.

FIG. 5D shows an example of a BP network flow 500D according toembodiments of the present disclosure. BP network flow 500D shows therelative initial supplies provided by each agent and demands required byeach contact type/skill combination. The total supply of 1 equals thetotal demand of 1.

FIG. 5E shows an example of a BP network flow 500E according toembodiments of the present disclosure. For ease of representation, thesupplies and demands have been scaled by a factor of 3000, and a maxflow solution for the initial supplies is shown for each edge. Accordingto this solution, edge 501A (from Agent 501 to Contact Type 511 withSkill 521) has an optimal flow of 900; edge 501B (from Agent 501 toContact Type 512 with Skill 521) has an optimal flow of 100; and edges501C and 501D have optimal flows of 0. Similarly, the optimal flows forAgent 502 are 300 and 700, respectively; and the optimal flows for Agent503 are 0 and 200, respectively.

According to this solution, Agent 503 may be substantially underutilizedrelative to Agents 501 and 502. Whereas Agents 501 and 502 are optimizedfor their full supplies of 1000 units each, Agent 503 is only expectedto use 200 units, or one-fifth of Agent 503's supply. In a contactcenter environment, Agent 503 may be assigned to fewer contacts andspend more time idle relative to Agents 501 and 502, or agents may beassigned non-preferred contacts, resulting in a lower contact centerperformance than the performance predicted by the max flow solution.

Similarly, according to this solution, contacts of Contact Type 512requiring Skill 521 may be substantially underutilized (or“underserved”) relative to the other contact type/skill combinations.Whereas the other contact type/skill combinations are optimized fortheir full demands of 900, 300, and 900 units, respectively, ContactType 512 requiring Skill 521 is only expected to receive 100 units, orone-ninth of this contact type/skill's demand. In a contact centerenvironment, this underutilized contact type/skill combination mayexperience longer wait times relative to other contact type/skillcombinations, or contacts may be assigned to non-preferred agents,resulting in a lower contact center performance than the performancepredicted by the max flow solution.

The solution shown in BP network flow 500E still balances total supplyand demand, but Agent 503 may be selected much less frequently than itspeers, and/or some contacts may need to wait much longer for a preferredagent, and/or the overall contact center performance may not achieve theoverall payout expected by the max flow solution.

FIGS. 5F and 5G show a technique of some embodiments for adjustingrelative agent supplies to improve the balance of agent and contactutilization in a contact center system where the max flow solution isunbalanced, as in BP network flow 500E (FIG. 5E).

FIG. 5F shows an example of a BP network flow 500F according toembodiments of the present disclosure. In BP network flow 500F, agentssharing the same skill sets have been “collapsed” into a single networknode. In this example, Agent 502 and Agent 503 have been combined into asingle node for Skill 522 with a combined total supply of 2000.

Similarly, contact types sharing the same skill sets have been collapsedinto single network nodes. In this example, Contact Types 511 and 512requiring Skill 521 have been combined into a single node for Skill 521with a combined total demand of 1800, and Contact Types 511 and 512requiring Skill 522 have been combined into a single node for Skill 522with a combined total demand of 1200.

Furthermore, the edges have been collapsed. For example, the four edgesemanating from Agents 502 and 503 (edges 502A, 502B, 503A, and 503B aslabeled in FIG. 5B) have been collapsed into a single edge emanatingfrom the “super node” for agents having Skill 522 to the super node” forcontact types requiring Skill 522.

At this point, in some embodiments, a quadratic programming algorithm orsimilar technique may be applied to the collapsed network to adjust therelative supplies of the agents.

FIG. 5G shows an example of a BP network flow 500G according toembodiments of the present disclosure. BP network flow 500G shows theadjusted agent supplies according to a solution to a quadraticprogramming algorithm or similar technique. In this example, the supplyfor the agent super node for Skills 521 and 522 has been adjusted from1000 in BP network flow 500F (FIG. 5F) to 1800, and the supply for theagent super node for Skill 522 has been adjusted from 2000 in BP networkflow 500F to 1200.

The total supply may remain the same (e.g., 3000 in this example), butthe relative supplies for agents of various skill sets has beenadjusted. In some embodiments, the total supply for a single super nodemay be distributed evenly among the agents within the super node. Inthis example, the 1200 units of supply for the agent super node forSkill 522 has been divided evenly among the agents, allocating 600 unitsto each of Agents 502 and 503.

FIG. 5H shows an example of a BP network flow 500H according toembodiments of the present disclosure. BP network flow 500H shows a maxflow solution computed using the adjusted supplies shown in BP networkflow 500G (FIG. 5G). Agent 501 has an adjusted supply of 1800, Agent 502has an adjusted supply of 600, and Agent 503 has an adjusted supply of600. According to this solution, edge 501A (from Agent 501 to ContactType 511 with Skill 521) still has an optimal flow of 900; edge 501B(from Agent 501 to Contact Type 512 with Skill 521) now has an optimalflow of 900; and edges 501C and 501D still have optimal flows of 0.Similarly, the optimal flows for Agent 502 are now 300 and 300 each; andthe optimal flows for Agent 503 are now 0 and 600, respectively.

FIG. 5I shows an example of a BP network flow 500I according toembodiments of the present disclosure. BP network flow 500I is identicalto BP network flow 500H except, for clarity, edges for which the optimalflow solution was determined to be 0 have been removed. In this example,edges 501C, 501D, and 503A have been removed.

Using the solution shown in BP network flows 500H and 500I, now allcontact type/skill combinations may be fully utilized (fully served).

Additionally, overall agent utilization may become more balanced. UnderBP network flow 500E (FIG. 5E), Agent 503 may have only been utilizedone-fifth as much as Agents 501 and 502. Thus, Agents 501 and 502 wouldhave been assigned approximately 45% of the contacts each, while Agent503 would have been assigned only the remaining approximately 10% of thecontacts. Under BP network flow 500H, Agent 501 may be assignedapproximately 60% of the contacts, and Agents 502 and 503 may beassigned approximately 20% each of the remaining contacts. In thisexample, the busiest agent (Agent 501) would only receive three times asmany contacts as the least busy agents (Agents 502 and 503), instead ofreceiving five times as many contacts.

FIG. 6 depicts a flow diagram of a BP skill-based payout matrix method600 according to embodiments of the present disclosure. BP skill-basedpayout matrix method 600 may begin at block 610.

At block 610, historical contact-agent outcome data may be analyzed. Insome embodiments, a rolling window of historical contact-agent outcomedata may be analyzed, such as a one-week, one-month, ninety-day, orone-year window. Historical contact-agent outcome data may includeinformation about individual interactions between a contact and anagent, including identifiers of which agent communicated with whichcontact, when the communication took place, the duration of thecommunication, and the outcome of the communication. For example, in atelesales call center, the outcome may indicate whether a sale occurredor the dollar amount of a sale, if any. In a customer retention queue,the outcome may indicate whether a customer was retained (or “saved”) orthe dollar value of any incentive offered to retain the customer. In acustomer service queue, the outcome may indicate whether the customer'sneeds were met or problems were solved, or a score (e.g., Net PromoterScore or NPS) or other rating representative of the customer'ssatisfaction with the contact-agent interaction. After—or in parallelwith—analyzing historical contact-agent outcome data, BP skill-basedpayout matrix method 600 may proceed to block 620.

At block 620, contact attribute data may be analyzed. Contact attributedata may include data stored in one or more customer relationshipmanagement (CRM) databases. For example, a wireless telecommunicationprovider's CRM database may include information about the type ofcellphone a customer uses, the type of contract the customer signed upfor, the duration of the customer's contract, the monthly price of thecustomer's contract, and the tenure of the customer's relationship withthe company. For another example, a bank's CRM database may includeinformation about the type and number of accounts held by the customer,the average monthly balance of the customer's accounts, and the tenureof the customer's relationship with the company. In some embodiments,contact attribute data may also include third party data stored in oneor more databases obtained from a third party. After—or in parallelwith—analyzing contact attribute data, BP skill-based payout matrixmethod 600 may proceed to block 630.

At block 630, skill groups may be determined for each agent and eachcontact type. Examples of skills include broad skills such as technicalsupport, billing support, sales, retention, etc.; language skills suchas English, Spanish, French, etc.; narrower skills such as “Level 2Advanced Technical Support,” technical support for Apple iPhone users,technical support for Google Android users, etc.; and any variety ofother skills. In some embodiments, there may not be any distinctiveskills, or only one skill may be identified across all of the agents orall of the contact types. In these embodiments, there may be only asingle “skill group.”

In some embodiments, a given contact type may require different skillsets at different times. For example, during a first call to a callcenter, a contact of one type might have a technical question andrequire an agent with a technical support skill, but during a secondcall, the same contact of the same type might have a billing questionand require an agent with a customer support skill. In theseembodiments, the same contact type may be included more than onceaccording to each contact type/skill combination. After skill groupshave been determined, BP skill-based payout matrix method 600 mayproceed to block 640.

At block 640, a target utilization may be determined for each agent, andan expected rate may be determined for each contact type (or contacttype/skill combinations). In some L1 environments, a balanced agentutilization may be targeted, such that each agent is expected to beassigned an approximately equal number of contacts over time. Forexample, if a contact center environment has four agents, each agent mayhave a target utilization of ¼ (or 25%). As another example, if acontact center environment has n agents, each agent may have a targetutilization of 1/n (or the equivalent percentage of contacts).

Similarly, expected rates for each contact type/skill may be determinedbased, for example, on the actual rates observed in the historicalcontact-agent outcome data analyzed at block 610. After targetutilization and expected rates have been determined, BP skill-basedpayout matrix method 600 may proceed to block 650.

At block 650, a payout matrix with expected payouts for each feasiblecontact-agent pairing may be determined. In some embodiments, acontact-agent pairing may be feasible if an agent and contact type haveat least one skill in common. In other embodiments, a contact-agentpairing may be feasible if an agent has at least all of the skillsrequired by the contact type. In yet other embodiments, other heuristicsfor feasibility may be used.

An example of a payout matrix is BP skill-based payout matrix 400A,described in detail above with reference to FIG. 4A. BP skill-basedpayout matrix 400A includes a set of agents with associated skills andtarget utilizations, a set of contact types (combined with various skillsets) with expected frequencies determined based on historicalcontact-agent outcome data and/or contact attribute data, and a set ofnon-zero expected payouts for each feasible contact-agent pairing. Afterthe payout matrix has been determined, BP skill-based payout matrixmethod 600 may proceed to block 660.

At block 660 a computer processor-generated model according to thepayout matrix may be outputted. For example, a computer processorembedded within or communicatively coupled to the contact center systemor a component therein such as a BP module may output the payout matrixmodel to be received by another component of the computer processor orthe contact center system. In some embodiments, the payout matrix modelmay be logged, printed, displayed, transmitted, or otherwise stored forother components or human administrators of the contact center system.After the payout matrix model has been outputted, BP skill-based payoutmatrix method 600 may end.

FIG. 7A shows a flow diagram of a BP network flow method 700A accordingto embodiments of the present disclosure. BP network flow method 700Amay begin at block 710.

At block 710, a BP payout matrix may be determined. In some embodiments,the BP payout matrix may be determined using BP payout matrix method 600or similar methods. In other embodiments, the BP payout matrix may bereceived from another component or module. After the BP payout matrixhas been determined, BP network flow method 700A may proceed to block720.

At block 720, a target utilization may be determined for each agent andexpected rates may be determined for each contact type. In otherembodiments, the payout matrix determined at block 710 may incorporateor otherwise include target utilizations and/or expected rates, such asa payout matrix outputted by BP payout matrix method 600, or BPskill-based payout matrix 400A (FIG. 4A). After target utilizations andexpected rates have been determined, if necessary, BP network flowmethod 700A may proceed to block 730.

At block 730, agent supplies and contact type demands may be determined.As described in detail above with reference to, for example, FIGS. 4Dand 4E, each agent may provide a “supply” equivalent to the expectedavailability or target utilization of each agent (e.g., in anenvironment with three agents, one-third each, for a total supply of 1or 100%). Additionally, each contact type/skill may demand an amount ofagent supply equivalent to the expected frequency or target utilizationof each contact type/skill, for a total demand of 1 or 100%. The totalsupply and demand may be normalized or otherwise configured to equal oneanother, and the capacity or bandwidth along each edge may be consideredinfinite or otherwise unlimited. In other embodiments, there may be asupply/demand imbalance, or there may be quotas or otherwise limitedcapacities set for some or all edges.

In some embodiments, the supplies and demands may be scaled by somefactor, e.g., 1000, 3000, etc. In doing so, the supply for each of threeagents may be shown to be 1000 instead of one-third, and the totalsupply may be shown to be 3000. Similarly, the relative demands for eachcontact type/skill set may be scaled. In some embodiments, no scalingoccurs. After agent supplies and contact type demands have beendetermined, BP network flow method 700A may proceed to block 740.

At block 740, preferred contact-agent pairings may be determined. Asdescribed in detail above with reference to, for example, FIGS. 4F and4G, one or more solutions for the BP network flow may be determined. Insome embodiments, a “maximum flow” or “max flow” algorithm, or otherlinear programming algorithm, may be applied to the BP network flow todetermine one or more solutions for optimizing the “flow” or“allocation” of the supplies (sources) to satisfy the demands (sinks).In some embodiments, a “max cost” algorithm may be applied to select anoptimal max flow solution.

In some contact center environments, such as an L2 (contact surplus)environment, the network flow may be reversed, so that contacts waitingin queue are the sources providing supplies, and the possible agentsthat may become available are the sinks providing demands.

The BP network flow may include an optimal flow solution determined by aBP module or similar component. According to this solution, of whichthere could be several to choose among, or to be selected at random,some (feasible) edges may have an optimal flow of 0, indicating thatsuch a feasible pairing is not a preferred pairing. In some embodiments,the BP network flow may remove edges representing feasible pairings ifthe pairing is determined to not be a preferred pairing.

Other edges may have a non-zero optimal flow, indicating that such afeasible pairing is preferred at least some of the time. As explained indetail above, this optimal flow solution describes the relativeproportion of contact-agent interactions (or the relative likelihoods ofselecting particular contact-agent interactions) that will achieve thetarget utilization of agents and contacts while also maximizing theexpected overall performance of the contact center system according tothe payouts for each pair of agent and contact type/skill set.

For some solutions of some BP network flows, a single contact type/skillmay have multiple edges flowing into it from multiple agents. In theseenvironments, the contact type/skill may have multiple preferredpairings. Given a choice among multiple agents, the BP network flowindicates the relative proportion or weighting for which one of theseveral agents may be selected each time a contact of that contacttype/skill arrives at the contact center. After determining preferredcontact-agent pairings, BP network flow method 700A may proceed to block750.

At block 750, a computer processor-generated model according to thepreferred contact-agent pairings may be outputted. For example, acomputer processor embedded within or communicatively coupled to thecontact center system or a component therein such as a BP module mayoutput the preferred pairings model to be received by another componentof the computer processor or the contact center system. In someembodiments, the preferred pairings model may be logged, printed,displayed, transmitted, or otherwise stored for other components orhuman administrators of the contact center system. After the preferredpairings model has been outputted, BP network flow method 700A may end.

FIG. 7B shows a flow diagram of a BP network flow method 700B accordingto embodiments of the present disclosure. BP network flow 700B issimilar to BP network flow 700A described above with reference to FIG.7A. BP network flow method 700B may begin at block 710. At block 710, aBP payout matrix may be determined. After the BP payout matrix has beendetermined, BP payout matrix method 700B may proceed to block 720. Atblock 720, a target utilization may be determined for each agent andexpected rates may be determined for each contact type. After targetutilizations and expected rates have been determined, if necessary, BPnetwork flow method 700B may proceed to block 730. At block 730, agentsupplies and contact type demands may be determined. After agentsupplies and contact type demands have been determined, BP network flowmethod 700B may proceed to block 735.

At block 735, agent supplies and/or contact demands may be adjusted tobalance agent utilization, or to improve agent utilization balance. Asdescribed in detail above with reference to, for example, FIGS. 5F and5G, agents sharing the same skill sets may be “collapsed” into singlenetwork nodes (or “super nodes”). Similarly, contact types sharing thesame skill sets may be collapsed into single network nodes. Furthermore,the edges may be collapsed according to their corresponding super nodes.At this point, in some embodiments, a quadratic programming algorithm orsimilar technique may be applied to the collapsed network to adjust therelative supplies of the agents and/or the relative demands of thecontacts. After adjusting agent supplies and/or contact demands tobalance agent utilization, BP network flow method 700B may proceed toblock 740.

At block 740, preferred contact-agent pairings may be determined. Afterdetermining preferred contact-agent pairings, BP network flow method700A may proceed to block 750. At block 750, a computerprocessor-generated model according to the preferred contact-agentpairings may be outputted. After the preferred pairings model has beenoutputted, BP network flow method 700B may end.

FIG. 8 shows a flow diagram of a BP network flow method 800 according toembodiments of the present disclosure. BP network flow method 800 maybegin at block 810.

At block 810, available agents may be determined. In a real-world queueof a contact center system, there may be dozens, hundreds, or thousandsof agents or more employed. At any given time, a fraction of theseemployed agents may be logged into the system or otherwise activelyworking on a shift. Also at any given time, a fraction of logged-inagents may be engaged in a contact interaction (e.g., on a call for acall center), logging the outcome of a recent contact interaction,taking a break, or otherwise unavailable to be assigned to incomingcontacts. The remaining portion of logged-in agents may be idle orotherwise available to be assigned. After determining the set ofavailable agents, BP network flow method 800 may proceed to block 820.

At block 820, a BP model of preferred contact-agent pairings may bedetermined. In some embodiments, the preferred pairings model may bedetermined using BP network flow method 700A (FIG. 7A) or 700B (FIG.7B), or similar methods. In other embodiments, the preferred pairingsmodel may be received from another component or module.

In some embodiments, the preferred pairings model may include all agentsemployed for the contact center queue or queues. In other embodiments,the preferred pairings model may include only those agents logged intothe queue at a given time. In still other embodiments, the preferredpairings model may include only those agents determined to be availableat block 810. For example, with reference to FIG. 4B, if Agent 403 isunavailable, some embodiments may use a different preferred pairingsmodel that omits a node for Agent 403 and includes nodes only foravailable agents Agent 401 and Agent 402. In other embodiments, thepreferred pairings model may include a node for Agent 403 but may beadapted to avoid generating a nonzero probability of assigning a contactto Agent 403. For example, the capacity of the flow from Agent 403 toeach compatible contact type may be set to zero.

The preferred pairings model may be precomputed (e.g., retrieved from acache or other storage) or computed in real-time or near real-time asagents become available or unavailable, and/or as contacts of varioustypes with various skill needs arrive at the contact center. After thepreferred pairings model has been determined, BP network flow method 800may proceed to block 830.

At block 830, an available contact may be determined. For example, in anL1 environment, multiple agents are available and waiting for assignmentto a contact, and the contact queue is empty. When a contact arrives atthe contact center, the contact may be assigned to one of the availableagents without waiting on hold. In some embodiments, the preferredpairings model determined at block 820 may be determined for the firsttime or updated after the determination of an available contact at block830. For example, with reference to FIGS. 4A-4G, Agents 401-403 may bethe three agents out of dozens or more that happen to be available at agiven moment. At that time, BP skill-based payout matrix 400A (FIG. 4A)may be determined for the three instant available agents, and BP networkflow 400G (FIG. 4G) may be determined for the three instant availableagents based on the BP skill-based payout matrix 400A. Thus, thepreferred pairings model may be determined at that time for those threeavailable agents.

In some embodiments, the preferred pairings model may account for someor all of the expected contact type/skill combinations as in, forexample, BP network flow 400G, even though the particular contact to bepaired is already known to BP network flow method 800 because thecontact has already been determined at block 830. After the availablecontact has been determined at block 830 (and the preferred pairingsmodel has been generated or updated, in some embodiments), the BPnetwork flow method 800 may proceed to block 840.

At block 840, at least one preferred contact-agent pairing among theavailable agents and the available contact may be determined. Forexample, as shown in BP network flow 400G (FIG. 4G), if the availablecontact is of Contact Type 411 and requires Skill 421 or 422, thepreferred pairing is to Agent 402. Similarly, if the available contactis of Contact Type 412 and requires Skill 421 or 422, the preferredpairings are to either Agent 401 (optimal flow of 400) or Agent 402(optimal flow of 50). After at least one preferred contact-agent pairinghas been determined, BP network flow method 800 may proceed to block850.

At block 850, one of the at least one preferred contact-agent pairingsmay be selected. In some embodiments, the selection may be at random,such as by using a pseudorandom number generator. The likelihood (orprobability) of selecting a given one of the at least one preferredcontact-agent pairings may be based on statistical likelihoods describedby the BP model. For example, as shown in BP network flow 400G (FIG.4G), if the available contact is of Contact Type 412 and requires Skill421 or 422, the probability of selecting Agent 401 is 400/450≈89%chance, and the probability of selecting Agent 402 is 50/450≈11% chance.

If there is only one preferred contact-agent pairing, there may be noneed for random selection in some embodiments as the selection may betrivial. For example, as shown in BP network flow 400G (FIG. 4G), if theavailable contact is of Contact Type 411 and requires Skill 421 or 422,the preferred pairing is always to Agent 402, and the probability ofselecting Agent 402 is 450/450=100% chance. After selecting one of theat least one preferred contact-agent pairings, BP network flow method800 may proceed to block 860.

At block 860, the selected pairing may be outputted for connection inthe contact center system. For example, a computer processor embeddedwithin or communicatively coupled to the contact center system or acomponent therein such as a BP module may output the preferred pairingselection (or recommended pairing, or pairing instruction) to bereceived by another component of the computer processor or the contactcenter system. In some embodiments, the preferred pairing selection maybe logged, printed, displayed, transmitted, or otherwise stored forother components or human administrators of the contact center system.The receiving component may use the preferred pairing selection to causethe selected agent to be connected to the contact for which a pairingwas requested or otherwise determined. After the preferred pairinginstruction has been outputted, BP network flow method 800 may end.

FIG. 9 shows a flow diagram of a BP network flow method 900 according toembodiments of the present disclosure. In some embodiments, BP networkflow method 900 is similar to BP network flow method 800. Whereas BPnetwork flow method 800 illustrates an L1 environment (agent surplus),BP network flow method 900 illustrates an L2 environment (contacts inqueue). BP network flow method 900 may begin at block 910.

At block 910, available contacts may be determined. In a real-worldqueue of a contact center system, there may be dozens, hundreds, etc. ofagents employed. In L2 environments, all logged-in agents are engaged incontact interactions or otherwise unavailable. As contacts arrive at thecontact center, the contacts may be asked to wait in a hold queue. At agiven time, there may be dozens or more contacts waiting on hold. Insome embodiments, the queue may be ordered sequentially by arrival time,with the longest-waiting contact at the head of the queue. In otherembodiments, the queue may be ordered at least in part based on apriority rating or status of individual contacts. For example, a contactdesignated as “high priority” may be positioned at or near the head ofthe queue, ahead of other “normal priority” contacts that have beenwaiting longer. After determining the set of available contacts waitingin queue, BP network flow method 900 may proceed to block 920.

At block 920, a BP model of preferred contact-agent pairings may bedetermined. In some embodiments, the preferred pairings model may bedetermined using a method similar to BP network flow method 700A (FIG.7A) or 700B (FIG. 7B), insofar as the waiting contacts provide thesources of supply, and an agents that may become available provide thesinks of demand. In other embodiments, the preferred pairings model maybe received from another component or module.

In some embodiments, the preferred pairings model may include allcontact types expected to arrive at the contact center queue or queues.In other embodiments, the preferred pairings model may include onlythose contact type/skill combinations present and waiting in the queueat the time the model was requested. For example, consider a contactcenter system that expects to receive contacts of three types X, Y, andZ, but only contacts of types X and Y are presently waiting in thequeue. Some embodiments may use a different preferred pairings modelthat omits a node for contact type Z, including nodes only for waitingcontacts of types X and Y. In other embodiments, the preferred pairingsmodel may include a node for contact type Z, but this model may beadapted to avoid generating a nonzero probability of assigning an agentto a contact of contact type Z. For example, the capacity of the flowfrom contact type Z to each compatible agent may be set to zero.

The preferred pairings model may be precomputed (e.g., retrieved from acache or other storage) or computed in real-time or near real-time asagents become available or unavailable, and/or as contacts of varioustypes with various skill needs arrive at the contact center. After thepreferred pairings model has been determined, BP network flow method 900may proceed to block 930.

At block 930, an available agent may be determined. For example, in anL2 environment, multiple contacts are waiting and available forassignment to an agent, and all agents may be occupied. When an agentbecomes available, the agent may be assigned to one of the waitingcontacts without remaining idle. In some embodiments, the preferredpairings model determined at block 920 may be determined for the firsttime or updated after the determination of an available agent at block830. For example, there may be three contacts waiting in queue, each ofa different skill and type. a BP skill-based payout matrix may bedetermined for the three instant waiting contacts, and a BP network flowmay be determined for the three instant waiting contacts based on the BPskill-based payout matrix. Thus, the preferred pairings model may bedetermined at that time for those three waiting contacts.

In some embodiments, the preferred pairings model may account for someor all of the potentially available agents, even though the particularagent to be paired is already known to BP network flow method 900because the agent has already been determined at block 930. After theavailable agent has been determined at block 930 (and the preferredpairings model has been generated or updated, in some embodiments), theBP network flow method 900 may proceed to block 940.

At block 940, at least one preferred contact-agent pairing among theavailable agent and the available contacts may be determined. After atleast one preferred contact-agent pairing has been determined, BPnetwork flow method 900 may proceed to block 950.

At block 950, one of the at least one preferred contact-agent pairingsmay be selected. In some embodiments, the selection may be at random,such as by using a pseudorandom number generator. The likelihood (orprobability) of selecting a given one of the at least one preferredcontact-agent pairings may be based on statistical likelihoods describedby the BP model. If there is only one preferred contact-agent pairing,there may be no need for random selection in some embodiments as theselection may be trivial. After selecting one of the at least onepreferred contact-agent pairings, BP network flow method 900 may proceedto block 960.

At block 960, the selected pairing may be outputted for connection inthe contact center system. For example, a computer processor embeddedwithin or communicatively coupled to the contact center system or acomponent therein such as a BP module may output the preferred pairingselection (or recommended pairing, or pairing instruction) to bereceived by another component of the computer processor or the contactcenter system. In some embodiments, the preferred pairing selection maybe logged, printed, displayed, transmitted, or otherwise stored forother components or human administrators of the contact center system.The receiving component may use the preferred pairing selection to causethe selected agent to be connected to the contact for which a pairingwas requested or otherwise determined. After the preferred pairinginstruction has been outputted, BP network flow method 900 may end.

In some embodiments, a BP payout matrix and network flow model may beused in L3 environments (i.e., multiple agents available and multiplecontacts waiting in queue). In some embodiments, the network flow modelmay be used to batch-pair multiple contact-agent pairingssimultaneously. BP pairing under L3 environments is described in detailin, for example, U.S. patent application Ser. No. 15/395,469, which isincorporated by reference herein. In other embodiments, a BP networkflow model may be used when a contact center system is operating in L1and/or L2 environments, and an alternative BP pairing strategy when thecontact center system is operating in L3 (or L0) environments.

In the examples described above, the BP network flow model targets abalanced agent utilization (or as close to balanced as would be feasiblefor a particular contact center environment). In other embodiments, askewed or otherwise unbalanced agent utilization may be targeted (e.g.,“Kappa” techniques), and/or a skewed or otherwise unbalanced contactutilization may be targeted (e.g., “Rho” techniques). Examples of thesetechniques, including Kappa and Rho techniques, are described in detailin, e.g., the aforementioned U.S. patent application Ser. Nos.14/956,086 and 14/956,074, which have been incorporated by referenceherein.

In some embodiments, such as those in which a BP module (e.g., BP module140) is fully embedded or otherwise integrated within a contact centerswitch (e.g., central switch 110, contact center switch 120A, etc.), theswitch may perform BP techniques without separate pairing requests andresponses between the switch and a BP module. For example, the switchmay determine its own cost function or functions to apply to eachpossible pairing as the need arises, and the switch may automaticallyminimize (or, in some configurations, maximize) the cost functionaccordingly. The switch may reduce or eliminate the need for skillqueues or other hierarchical arrangements of agents or contacts;instead, the switch may operate across one or more virtual agent groupsor sets of agents among a larger pool of agents within the contactcenter system. Some or all aspects of the BP pairing methodology may beimplemented by the switch as needed, including data collection, dataanalysis, model generation, network flow optimization, etc.

In some embodiments, such as those optimizing virtual agent groups,models of agent nodes in network flows may represent sets of agentshaving one or more agent skill/type combinations for agents foundanywhere within the contact center system, regardless of whether thecontact center system assigns agents to one or more skill queues. Forexample, the nodes for Agents 401, 402, and 403 in FIGS. 4B-4G mayrepresent virtual agent groups instead of individual agents, and acontact assigned to a virtual agent group may be subsequently assignedto an individual agent within the virtual agent group (e.g., randomassignment, round-robin assignment, model-based behavioral pairing,etc.). In these embodiments, BP may be applied to a contact at a higherlevel within the contact center system (e.g., central switch 101 in FIG.1), before a contact is filtered or otherwise assigned to an individualskill queue and/or agent group (e.g., either contact center switch 120Aor contact center switch 120B in FIG. 1).

The application of BP earlier in the process may be advantageous insofaras it avoids scripts and other prescriptive techniques that conventionalcentral switches use to decide to which queue/switch/VDN a contactshould be assigned. These scripts and other prescriptive techniques maybe inefficient and suboptimal both in terms of optimizing overallcontact center performance and achieving a desired target agentutilization (e.g., balanced agent utilization, minimal agent utilizationimbalance, a specified amount agent utilization skew).

At this point it should be noted that behavioral pairing in a contactcenter system in accordance with the present disclosure as describedabove may involve the processing of input data and the generation ofoutput data to some extent. This input data processing and output datageneration may be implemented in hardware or software. For example,specific electronic components may be employed in a behavioral pairingmodule or similar or related circuitry for implementing the functionsassociated with behavioral pairing in a contact center system inaccordance with the present disclosure as described above.Alternatively, one or more processors operating in accordance withinstructions may implement the functions associated with behavioralpairing in a contact center system in accordance with the presentdisclosure as described above. If such is the case, it is within thescope of the present disclosure that such instructions may be stored onone or more non-transitory processor readable storage media (e.g., amagnetic disk or other storage medium), or transmitted to one or moreprocessors via one or more signals embodied in one or more carrierwaves.

The present disclosure is not to be limited in scope by the specificembodiments described herein. Indeed, other various embodiments of andmodifications to the present disclosure, in addition to those describedherein, will be apparent to those of ordinary skill in the art from theforegoing description and accompanying drawings. Thus, such otherembodiments and modifications are intended to fall within the scope ofthe present disclosure. Further, although the present disclosure hasbeen described herein in the context of at least one particularimplementation in at least one particular environment for at least oneparticular purpose, those of ordinary skill in the art will recognizethat its usefulness is not limited thereto and that the presentdisclosure may be beneficially implemented in any number of environmentsfor any number of purposes. Accordingly, the claims set forth belowshould be construed in view of the full breadth and spirit of thepresent disclosure as described herein.

The invention claimed is:
 1. A method for behavioral pairing modelevaluation in a contact center system comprising: determining, by atleast one computer processor communicatively coupled to and configuredto perform behavioral pairing operations in the contact center system, aplurality of agents and a plurality of contact types; analyzing, by theat least one computer processor, historical contact-agent outcome datato determine an expected value of each feasible combination of agent andcontact type from the pluralities of agents and contact types;determining, by the at least one computer processor, a pairing modelbased on the expected values of feasible combinations; determining, bythe at least one computer processor, an expected performance of thecontact center system using the pairing model; outputting, by the atleast one computer processor, the expected performance of the contactcenter system using the pairing model; and establishing, in a switchmodule of the contact center system, a communication channel between acontact and an agent based at least in part upon the pairing model. 2.The method of claim 1, wherein the pairing model can be represented as apayout matrix.
 3. The method of claim 1, further comprising:determining, by the at least one computer processor, an expectedfrequency for each contact type of the plurality of contact types,wherein the pairing model is further based on the expected frequency foreach contact type.
 4. The method of claim 1, further comprising:determining, by the at least one computer processor, a targetutilization for each agent of the plurality of agents, wherein thepairing model is further based on the target utilization for each agent.5. The method of claim 4, wherein the pairing model targets a balancedagent utilization.
 6. The method of claim 1, wherein each feasiblecombination comprises an agent with at least a first skill and a contacttype with at least a first need corresponding to the first skill.
 7. Themethod of claim 1, further comprising: determining, by the at least onecomputer processor, a probabilistic network flow model based on thepairing model.
 8. The method of claim 7, wherein the probabilisticnetwork flow model comprises: supply nodes, wherein each supply node isan agent of the plurality of agents or an agent group comprising asubset of agents of the plurality of agents; demand nodes, wherein eachdemand node is a contact type of the plurality of contact types or acontact type group comprising a subset of contact types of the pluralityof contact types.
 9. The method of claim 8, wherein the probabilisticnetwork flow model comprises: supply values associated with each of thesupply nodes corresponding to target utilizations for at least one agentof the plurality of agents.
 10. The method of claim 8, wherein theprobabilistic network flow model comprises: demand values associatedwith each of the demand nodes corresponding to expected frequencies forat least one contact type of the plurality of contact types.
 11. Themethod of claim 7, wherein the probabilistic network flow modecomprises: a plurality of edges between supply nodes and demand nodes,wherein each edge of the plurality of edges indicates one of eachfeasible combination.
 12. The method of claim 7, wherein theprobabilistic network flow model comprises: a plurality of edge weights,wherein each edge weight of the plurality of edge weights indicates theexpected value of a corresponding feasible combination of agent andcontact type.
 13. A system for behavioral pairing model evaluation in acontact center system comprising: at least one computer processorcommunicatively coupled to and configured to perform behavioral pairingoperations in the contact center system, wherein the at least onecomputer processor is further configured to: determine a plurality ofagents and a plurality of contact types; analyze historicalcontact-agent outcome data to determine an expected value of eachfeasible combination of agent and contact type from the pluralities ofagents and contact types; determine a pairing model based on theexpected values of feasible combinations; determine an expectedperformance of the contact center system using the pairing model; outputthe expected performance of the contact center system using the pairingmodel; and establish, in a switch module of the contact center system, acommunication channel between a contact and an agent based at least inpart upon the pairing model.
 14. The system of claim 13, wherein thepairing model can be represented as a payout matrix.
 15. The system ofclaim 13, wherein the at least one computer processor is furtherconfigured to: determine an expected frequency for each contact type ofthe plurality of contact types, wherein the pairing model is furtherbased on the expected frequency for each contact type.
 16. The system ofclaim 13, wherein the at least one computer processor is furtherconfigured to: determine a target utilization for each agent of theplurality of agents, wherein the pairing model is further based on thetarget utilization for each agent.
 17. The system of claim 16, whereinthe pairing model targets a balanced agent utilization.
 18. The systemof claim 13, wherein each feasible combination comprises an agent withat least a first skill and a contact type with at least a first needcorresponding to the first skill.
 19. The system of claim 13, whereinthe at least one computer processor is further configured to: determinea probabilistic network flow model based on the pairing model.
 20. Thesystem of claim 19, wherein the probabilistic network flow modelcomprises: supply nodes, wherein each supply node is an agent of theplurality of agents or an agent group comprising a subset of agents ofthe plurality of agents; demand nodes, wherein each demand node is acontact type of the plurality of contact types or a contact type groupcomprising a subset of contact types of the plurality of contact types.21. The system of claim 20, wherein the probabilistic network flow modelcomprises: supply values associated with each of the supply nodescorresponding to target utilizations for at least one agent of theplurality of agents.
 22. The system of claim 20, wherein theprobabilistic network flow model comprises: demand values associatedwith each of the demand nodes corresponding to expected frequencies forat least one contact type of the plurality of contact types.
 23. Thesystem of claim 19, wherein the probabilistic network flow modecomprises: a plurality of edges between supply nodes and demand nodes,wherein each edge of the plurality of edges indicates one of eachfeasible combination.
 24. The system of claim 19, wherein theprobabilistic network flow model comprises: a plurality of edge weights,wherein each edge weight of the plurality of edge weights indicates theexpected value of a corresponding feasible combination of agent andcontact type.
 25. An article of manufacture for behavioral pairing modelevaluation in a contact center system comprising: a non-transitoryprocessor readable medium; and instructions stored on the medium;wherein the instructions are configured to be readable from the mediumby at least one computer processor communicatively coupled to andconfigured to perform behavioral pairing operations in the contactcenter system and thereby cause the at least one computer processor tooperate so as to: determine a plurality of agents and a plurality ofcontact types; analyze historical contact-agent outcome data todetermine an expected value of each feasible combination of agent andcontact type from the pluralities of agents and contact types; determinea pairing model based on the expected values of feasible combinations;determine an expected performance of the contact center system using thepairing model; output the expected performance of the contact centersystem using the pairing model; and establish, in a switch module of thecontact center system, a communication channel between a contact and anagent based at least in part upon the pairing model.